Among the injured were three UN peacekeepers, two police officers from South Sudan and two civilian staff members, UN spokesman Stephane Dujarric told a press briefing.
He said the attack was carried out by unidentified gunmen and the patrol appeared to have been deliberately targeted.
The mission said it had deployed a "Quick Reaction Force" to secure the area and support the emergency response after the attack.
The patrol was going to the area of Pajut in the state of Jonglei when it came under attack.
"These are part of regular patrols that the UN has been doing in trying to help the constant insecurity in the area," Dujarric said.
The UN has called on relevant authorities for a thorough and prompt investigation to ensure all those responsible are brought to justice, Dujarric said.
He stressed that "attacks against UN peacekeepers may constitute war crimes under international law".
The latest violence "brings to nine the number of peacekeepers killed in malicious acts since January 1 of this year," he added.
Attacks on UN personnel are rare but not unprecedented in South Sudan, where UN patrols operate in volatile areas affected by intercommunal fighting, armed youth mobilisations and clashes involving government forces.
In June, the UN Security Council adopted a resolution aimed at strengthening accountability for attacks on UN peacekeepers, amid concern over rising violence and low prosecution rates.
That followed a series of incidents targeting UN personnel, including the killing of seven peacekeepers serving with the United Nations Interim Force in Lebanon after a fresh round of fighting broke out between Israel and Hezbollah in early March.
with AP
